sinusoidal stationary response

简明释义

正弦平稳响应

英英释义

例句

1.The sinusoidal stationary response of the circuit was measured using an oscilloscope.

使用示波器测量了电路的正弦稳态响应。

2.Engineers often analyze the sinusoidal stationary response to predict how systems will behave under regular conditions.

工程师们常常分析正弦稳态响应以预测系统在正常条件下的行为。

3.In control theory, understanding the sinusoidal stationary response is crucial for designing stable systems.

在控制理论中，理解正弦稳态响应对设计稳定系统至关重要。

4.The sinusoidal stationary response indicates that the system can handle sinusoidal inputs effectively.

该正弦稳态响应表明系统能够有效处理正弦输入。

5.The system exhibits a sinusoidal stationary response when subjected to periodic inputs.

当系统受到周期性输入时，表现出正弦稳态响应。

作文

In the field of engineering and physics, understanding dynamic systems is crucial for designing effective solutions. One important concept in this domain is the sinusoidal stationary response. This term refers to the behavior of a system when it is subjected to sinusoidal inputs at a constant frequency. Essentially, it describes how a system reacts over time when the input remains periodic and stable. To appreciate the significance of the sinusoidal stationary response, we must first delve into the nature of sinusoidal signals and the systems that process them.Sinusoidal signals are waveforms that oscillate smoothly and periodically. They can be represented mathematically as sine or cosine functions. These signals are fundamental in various fields, including electrical engineering, acoustics, and control systems. When a system is excited by a sinusoidal input, its response can vary significantly depending on its characteristics. The sinusoidal stationary response specifically pertains to the steady-state behavior of the system after any transient effects have dissipated.Transient responses occur when a system first encounters a change in input, such as when a sinusoidal signal is introduced. During this period, the system may exhibit fluctuations before settling into a consistent pattern. However, the focus of the sinusoidal stationary response is on the long-term behavior of the system, where it reaches equilibrium and consistently replicates the input signal's frequency and amplitude.One key aspect of analyzing the sinusoidal stationary response is determining the system's frequency response. This involves examining how different frequencies affect the output. For instance, in electrical circuits, the impedance of components like resistors, capacitors, and inductors will influence how the circuit responds to sinusoidal inputs. Engineers often use Bode plots to visualize this frequency response, which helps predict how a system will behave under various conditions.The sinusoidal stationary response also plays a vital role in control theory, where maintaining stability is essential. In feedback systems, the objective is to ensure that the output remains close to the desired input despite disturbances. By understanding the sinusoidal stationary response, engineers can design controllers that effectively manage these systems, ensuring they respond appropriately to sinusoidal inputs without oscillating excessively or becoming unstable.Moreover, the concept of sinusoidal stationary response is not limited to linear systems. Non-linear systems can also exhibit stationary responses, although their behavior may be more complex. In such cases, harmonic analysis may be employed to understand how non-linearities affect the system's response to sinusoidal inputs.In conclusion, the sinusoidal stationary response is a fundamental concept in the study of dynamic systems. It provides insights into how systems react to periodic inputs, allowing engineers and scientists to design better systems and controllers. By focusing on the steady-state behavior and frequency response, we gain a deeper understanding of the underlying principles governing these systems. Ultimately, mastering the concept of sinusoidal stationary response is essential for anyone involved in the fields of engineering and physics, as it lays the groundwork for more advanced studies and applications in dynamic system analysis.

在工程和物理领域，理解动态系统对于设计有效的解决方案至关重要。一个重要的概念是正弦稳态响应。这个术语指的是当一个系统受到恒定频率的正弦输入时的行为。它本质上描述了当输入保持周期性和稳定时，系统随时间的反应。为了欣赏正弦稳态响应的重要性，我们必须首先深入了解正弦信号的性质以及处理这些信号的系统。正弦信号是平滑且周期性振荡的波形。它们可以用正弦或余弦函数在数学上表示。这些信号在电气工程、声学和控制系统等多个领域中是基础。当一个系统受到正弦输入的激励时，它的响应可能会因其特性而显著变化。正弦稳态响应特别涉及系统在瞬态效应消散后的稳态行为。瞬态响应发生在系统首次遇到输入变化时，例如当引入正弦信号时。在此期间，系统可能会出现波动，随后才会稳定下来。然而，正弦稳态响应的重点是系统的长期行为，在这一阶段，系统达到平衡并始终如一地复制输入信号的频率和幅度。分析正弦稳态响应的一个关键方面是确定系统的频率响应。这涉及到检查不同频率如何影响输出。例如，在电路中，电阻器、电容器和电感器等元件的阻抗将影响电路对正弦输入的响应。工程师通常使用波特图来可视化这种频率响应，这有助于预测系统在各种条件下的行为。正弦稳态响应在控制理论中也发挥着重要作用，在那里保持稳定性至关重要。在反馈系统中，目标是确保输出在扰动的情况下仍然接近期望输入。通过理解正弦稳态响应，工程师可以设计有效管理这些系统的控制器，确保它们适当地响应正弦输入，而不会过度振荡或变得不稳定。此外，正弦稳态响应的概念不仅限于线性系统。非线性系统也可以表现出稳态响应，尽管它们的行为可能更加复杂。在这种情况下，谐波分析可能被用来理解非线性如何影响系统对正弦输入的响应。总之，正弦稳态响应是动态系统研究中的一个基本概念。它提供了关于系统如何响应周期性输入的见解，使工程师和科学家能够设计更好的系统和控制器。通过关注稳态行为和频率响应，我们对支配这些系统的基本原理有了更深入的理解。最终，掌握正弦稳态响应的概念对于任何参与工程和物理领域的人来说都是至关重要的，因为它为动态系统分析中的更高级研究和应用奠定了基础。